# Properties

 Label 2015.1.bq Level 2015 Weight 1 Character orbit bq Rep. character $$\chi_{2015}(464,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 16 Newform subspaces 5 Sturm bound 224 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2015 = 5 \cdot 13 \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2015.bq (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$2015$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$224$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(2015, [\chi])$$.

Total New Old
Modular forms 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 8 8 0 0

## Trace form

 $$16q - 4q^{4} - 4q^{9} + O(q^{10})$$ $$16q - 4q^{4} - 4q^{9} - 4q^{10} - 8q^{14} + 4q^{19} - 8q^{31} - 4q^{35} - 4q^{36} + 12q^{39} + 8q^{40} + 8q^{41} - 8q^{45} - 4q^{49} - 16q^{51} + 4q^{56} + 8q^{59} + 8q^{66} + 4q^{71} - 8q^{81} + 4q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(2015, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2015.1.bq.a $$2$$ $$1.006$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-155})$$ None $$0$$ $$-2$$ $$2$$ $$0$$ $$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots$$
2015.1.bq.b $$2$$ $$1.006$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-155})$$ None $$0$$ $$2$$ $$2$$ $$0$$ $$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots$$
2015.1.bq.c $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$$
2015.1.bq.d $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ $$D_{6}$$ $$\Q(\sqrt{-155})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\zeta_{12}^{2}q^{4}-q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots$$
2015.1.bq.e $$4$$ $$1.006$$ $$\Q(\zeta_{12})$$ $$A_{4}$$ None None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)
$3$ ($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)($$( 1 - T^{2} + T^{4} )^{2}$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)
$5$ ($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T )^{4}$$)($$( 1 + T^{2} )^{2}$$)
$7$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)
$11$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)
$13$ ($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$( 1 + T )^{4}$$)($$1 - T^{2} + T^{4}$$)($$( 1 - T )^{4}$$)
$17$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 + T )^{2}( 1 - T + T^{2} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)
$19$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)
$23$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 + T )^{2}( 1 - T + T^{2} )$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)
$29$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)
$31$ ($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 + T )^{4}$$)($$( 1 + T )^{4}$$)($$( 1 + T )^{4}$$)
$37$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 + T )^{2}( 1 - T + T^{2} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)
$41$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)
$43$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 + T )^{2}( 1 - T + T^{2} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)
$47$ ($$( 1 - T )^{2}( 1 + T )^{2}$$)($$( 1 - T )^{2}( 1 + T )^{2}$$)($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 - T )^{4}( 1 + T )^{4}$$)
$53$ ($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{4}$$)($$( 1 - T^{2} + T^{4} )^{2}$$)($$( 1 + T^{2} )^{4}$$)
$59$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)
$61$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)
$67$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)
$71$ ($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{2}( 1 + T + T^{2} )$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)($$( 1 + T )^{4}( 1 - T + T^{2} )^{2}$$)($$( 1 - T )^{4}( 1 + T + T^{2} )^{2}$$)
$73$ ($$( 1 - T )^{4}$$)($$( 1 + T )^{4}$$)($$( 1 + T^{2} )^{4}$$)($$( 1 + T^{2} )^{4}$$)($$( 1 + T^{2} )^{4}$$)
$79$ ($$( 1 - T )^{2}( 1 + T )^{2}$$)($$( 1 - T )^{2}( 1 + T )^{2}$$)($$( 1 + T^{2} )^{4}$$)($$( 1 - T )^{4}( 1 + T )^{4}$$)($$( 1 + T^{2} )^{4}$$)
$83$ ($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 - T )^{8}$$)($$( 1 - T^{2} + T^{4} )^{2}$$)($$( 1 + T )^{8}$$)
$89$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)
$97$ ($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 - T + T^{2} )( 1 + T + T^{2} )$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)($$( 1 - T + T^{2} )^{2}( 1 + T + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}( 1 - T^{2} + T^{4} )$$)